Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 670 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 125 sq cm (d) 25 sq cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
3. 3.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
9. 9.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 220 cu cm (b) 20 cu cm (c) 200 cu cm (d) 19 cu cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
11. 11.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
13. 13.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 12 cu cm (c) 60 cu cm (d) 20 cu cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
16. 16.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 190 sq cm (c) 380 sq cm (d) 95 sq cm
17. 17.A cuboid is 12 cm long, 10 cm wide and 9 cm high. What is its volume? (a) 1080 cu cm (b) 31 cu cm (c) 120 cu cm (d) 636 cu cm
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
19. 19.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
20. 20.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 294 cu cm (d) 343 cu cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
22. 22.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
23. 23.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
24. 24.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
25. 25.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
27. 27.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 144 cu cm (b) 24 cu cm (c) 16 cu cm (d) 168 cu cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
29. 29.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 16 sq cm (d) 8 sq cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
31. 31.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 32 cu cm (b) 64 cu cm (c) 10 cu cm (d) 8 cu cm
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
34. 34.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 150 sq cm (b) 95 sq cm (c) 380 sq cm (d) 190 sq cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
36. 36.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 134 sq cm (b) 268 sq cm (c) 536 sq cm (d) 240 sq cm
37. 37.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
38. 38.A cuboid is 8 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 161 sq cm (b) 392 sq cm (c) 644 sq cm (d) 322 sq cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
40. 40.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 16 cu cm (b) 90 cu cm (c) 18 cu cm (d) 146 cu cm

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